Answer:
The probability mass function is given by
P(X = 0) = 0.003, P(X = 1) = 0.164, P(X = 2) = 0.833
Step-by-step explanation:
Given to us are two mechanical components.
The probability of the first component meeting the given specifications are 0.98.
The probability that the second component meets the given specifications = 0.85.
In the information given the components are said to be independent.
The probability mass function will be calculated in the following way
i.) P(X=0) which is the probability that neither of the components meet the specifications.
ii) P(X=1) which is the probability when either of the components will meet the specifications and the other will not.
iii) P(X=2) which is the probability that both components meet the specification.
Therefore P(X = 0) = ( 1 - 0.98) × ( 1 - 0.85) = 0.02 × 0.15 = 0.003
and, P(X = 1) = (0.98 × ( 1 - 0.85)) + (( 1 - 0.98) × 0.85)
= (0.98 × 0.15) + (0.02 × 0.85)
= 0.147 + 0.017
= 0.164
and finally, P(X=2) = (0.98 × 0.85)
= 0.833
